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1.
A super deep issue; an excuse to your boss's so you don't have to explain yourself, as to why your not coming in. Like a personal issue but deeper!!
I can't come into work I am having a dissue!
by Whatitis August 18, 2013
 
2.
Also known as a dishpute, dissues are issues arising in shared accommodation about who should do the washing up.
"I've got dissues at home."

"Apologies about the dirty dishes, we're having some dissues at the moment."

"My housemate and I have had a dishpute."
by Riiichaaard February 23, 2009